RStudio Server requires root privileges for installation and certain operations. Note that root privileges are also required for installing R.
sudo yum install R
sudo yum install --nogpgcheck <rstudio-server-package.rpm>
RStudio Server runs as the system root user during startup and for creating R sessions on behalf of users.
Further details are explained in the admin guide:
RStudio Server runs as the system root user during startup and then drops this privilege and runs as a more restricted user. RStudio Server then re-assumes root privilege for a brief instant when creating R sessions on behalf of users (the server needs to call setresuid when creating the R session, and this call requires root privilege).
The user account that RStudio Server runs under in the normal course of operations is rstudio-server. This account is automatically added to the system during installation and is created as a system rather than end user account (i.e. the --system flag is passed to useradd).
One way to control the scope of root access is to install RStudio Server in a VM or docker. That way root access will be bound to the instance as opposed to the physical server.